IV.D User-Defined Fluid/Solid

DELTAE has a provision that allows users to specify `external' fluids or solids that are not part of the standard library of thermophysical properties. Properties are derived, according to current operating conditions, from Eqs. IV.1, IV.2 and IV.3 using coefficients read from a user-written text file. Up to five distinct external fluids and five external solids can be used at one time.

The file can have any name valid under the operating system under which DELTAE is running, and it should end with the extension .tpf. If the root filename is the same as any predefined fluids, DELTAE will replace it's internal calculations for that fluid with those given in the user file. To request a user-defined fluid, simply use the root file name as you would any other fluid. The .tpf file should be in the same directory or folder as the model file. The name of the fluid is set to the root filename of the external fluid file.

The file format is similar to the segment definitions we have used in models described in previous chapters in that comment lines can be added with an initial `!' and blank lines are ignored. Each property is specified by a line containing 1-10 real coefficients which are read in as C_0-9, where unused parameters are set to zero. It is critical that the properties be arranged as shown: . We also need the ratio of specific heats, , and the expansion coefficient , but these are calculated internally from

Each of the five properties is derived from its 10 coefficients using the following equation:

where T and p_m are the absolute temperature (K) and mean pressure (Pa) for each point at which a segment using the fluid is evaluated.

Equation IV.2 is a compromise between simplicity and flexibility; it is intended for use in a variety of simple expressions for gases and liquids and have a uniform syntax for specifying all 5 properties. There is only a limited mean pressure dependence suitable for ideal gases; for more complicated mean pressure dependence, multiple .tpf files should be written for each mean pressure range used.

To illustrate the use of these coefficients, consider the example below. To replace the (ideal) helium gas in a model with a more accurate representation that calculates density and sound speed using the first coefficient of the virial expansion for helium, we can write the following file, call it helium.tpf, and put it in the same directory as our model:

! external fluid; He with first virial coeff for (B=12cc/mole) 
! Equation is: 
! C0 + C1*pm/(T+C2*pm) + C3*T + C4*T^2 + C5*T^C6 + pm^2 *C7*T^C8 + pm*C9
! Density, rho (m^3):
  0.  4.814e-4 1.44e-6
! isobaric heat capacity, cp (J/kg/K):
  5192.
! Thermal conductivity, k0 (W/m/K):
 0. 0. 0. 0. 0. 0.0025672  0.716
! Square of sound speed, a^2 (m^2/s^2):
  0.  0.  0.  3461.92  0. 0. 0. 0.  0. .0100
! Viscosity, mu (kg/s/m):
 0. 0. 0. 0. 0. 0.412e-6  0.68014

so we set C_3 = R/M, and C_9 = 2B/M, where = 5/3. See section C.1 in Chapter V to compare this with how helium transport properties are calculated in DELTAE's internal routine.

For equations that cannot be manipulated to fit the format of Eq. iv.2, we suggest generating a table of data near the expected operating conditions and using curve-fitting tools to generate appropriate coefficients.

User-defined solids follow an identical format, except that only the first three lines are required to specify . The meanings of coefficients C_1 and C_2 are also redefined to provide an exponential capability, so the equation for solids is

It is a good idea to check each new external fluid or solid by using the (t)hermophysical command available in the main menu (external fluid or solids show up first and are selected with negative integers). Users can also insert the special THERMophysical segment using the fluid/solid to display the properties in the .out and .dat files, or to plot them (see below).